Question

Four integers are added to a group of integers 3,4,5, 5 and 8 and the mean, median, and
mode of the data increases by 1 each. What is the greatest integer in the new group of
integers?​

Answer 1

$\bf\large\underline\green{Solution :-}$

➤ The given integers are 3, 4, 5, 5 and 8.

Mean = (3 + 4 + 5 + 5 + 8)/5

= 25/5

Mean = 5

Median = 5

and Mode = 5 (Mode is the most frequently occurring value)

After adding 4 integers, mode is increased by 1,

Therefore, the new mode is 6.

Since, the mode is most frequently occurring value, there 6 must be added at least three times.

So, the new set of integers will be 3, 4, 5, 5, 6, 6, 6, 8 and x.

Let the 4th integers be 'x'.

And the new mean is 6.

6 = (3 + 4 + 5 + 5 + 6 + 6 + 6 + 8 + x)/9

(43 + x)/9 = 6

43 + x = 54

x = 54 - 43

x = 11

So, greatest of the four integers that are added is 11.

Answer.

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